Receivers for digital communications systems are becoming available which can handle several transmissions simultaneously. Such receivers typically make use of multiuser detection, commonly referred to as MUD. Multiuser detection is a means by which several signals, either completely or partially occupying a single communications channel, can be separated mathematically.
To operate, a MUD receiver must have the received data available, and must have knowledge of the basic waveform transmitted at each transmitter, as appearing in the receiver. This basic waveform is commonly referred to as a composite signature waveform. Each transmission's composite signature waveform is the waveform that would be present in the receiver, if only one data symbol had been transmitted by each transmitter individually. These waveforms each define a column in an ‘S’ matrix in the MUD receiver, sometimes called the signature matrix.
When a receiver is operating in an asynchronous environment with inter-symbol interference, the structure of the S-matrix becomes more complicated. In particular, the asynchronisity will delay individual columns of the S-matrix, causing signals which once lined-up to shift with respect to each other. Furthermore, an inter-symbol interference problem will be reflected in waveforms (columns of the S matrix) which extend beyond the boundaries of what is normally attributed to a symbol. These problems conspire to alter the way a multiuser detection system works.
In more detail, for a completely synchronous system, with waveforms that do not extend beyond the boundaries of a symbol decision, demodulation of a series of symbols can be accomplished without loss of optimality, by breaking the problem up into individual symbol-by-symbol demodulations. This is mathematically possible because the S matrix is block-diagonal, and the problem naturally separates. Referring to FIG. 1a, in such a completely synchronous case, the larger MUD problem r=S*b is separable into (as many bits are in a frame) several smaller problems, ri=S*b1. Each of the sub-matrices S are identical, and just shifted in time to make up the larger matrix S, which covers the whole frame of data.
However, in an asynchronous system, the MUD receiver is faced with an inseparability problem, where the columns of the S matrix are overlapping, mixing together the contributions of S*bi in the received data. As individual signals are allowed to be asynchronous, the waveforms due to each overlap in complicated ways, introducing dependencies amongst bit decisions. These dependencies typically inter-relate (a→b→c etc.) in such a way that even a small level asynchronous reception can result in a whole frame of data that has inter-related bits. This asynchronous situation is depicted in FIG. 1b. Note that the individual S sub-matrices making up S matrix are overlapping in time. Thus, a system of ensuring separability at the receiver must be employed, by limiting the time response of each transmission, combined with some means of synchronizing each source.
Achieving synchronization of the several sources at the receiver, however, is not trivial, and can be difficult to achieve. Resources of the system (as reflected in the overhead of transmitting control messages) must be spent to control the exact timing of each source. In addition, if the temporal response of each transmission must be reduced to further ensure the separability, this will result in a larger bandwidth of signal, which also spends resources of the system by reducing available frequency bands for transmission. Generally stated, demodulation of a frame's worth of data in an asynchronous system with inter-symbol interference is typically unfeasible. In all but academic situations, the MUD module needed in such a case would be prohibitively complicated.
What is needed, therefore, is a solution to the problem of the computational complexity of a multiuser detector (any variety) when a large number of symbols need to be jointly demodulated, and in particular, when either asynchronous reception or intersymbol interference is encountered.